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Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

Improving Translational Accuracy

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Base complementarity between the three base pairs of mRNA codon and the tRNA anticodon is not a failsafe mechanism. Inaccuracies can range from a single mismatch to no correct base pairing at all. The free energy difference between the correct and nearly correct base pairs can be as small as 3 kcal/ mol. With complementarity being the only proofreading step, the estimated error frequency would be one wrong amino acid in every 100 amino acids incorporated. However, error frequencies observed in...

Improving Translational Accuracy

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Base complementarity between the three base pairs of mRNA codon and the tRNA anticodon is not a failsafe mechanism. Inaccuracies can range from a single mismatch to no correct base pairing at all. The free energy difference between the correct and nearly correct base pairs can be as small as 3 kcal/ mol. With complementarity being the only proofreading step, the estimated error frequency would be one wrong amino acid in every 100 amino acids incorporated. However, error frequencies observed in...

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Related Experiment Videos

ReFIT: Federated Transfer Learning for Sequential Prediction and Uncertainty Quantification Using Streaming EHR Data.

Yuying Lu¹, Lan Luo², Tian Gu¹

¹Department of Biostatistics, Columbia Mailman School of Public Health, New York, NY 10032, USA.

Statistics in Biosciences

|July 9, 2026

Summary

This summary is machine-generated.

We developed a Renewable Federated Incremental Transfer (ReFIT) framework to integrate biomedical data from multiple sources. ReFIT improves prediction accuracy and quantifies uncertainty for limited target populations while preserving privacy.

Related Experiment Videos

Area of Science:

Biomedical Informatics
Machine Learning
Statistical Inference

Background:

Biomedical data collection is distributed across institutions and time.
Challenges include privacy, scalability, and data heterogeneity.
Knowledge transfer is key for improved statistical inference.

Purpose of the Study:

To propose a privacy-preserving framework for integrating streaming biomedical data.
To improve model estimation and prediction in target populations with limited samples.
To adapt to evolving data environments and distributional shifts.

Main Methods:

Renewable Federated Incremental Transfer (ReFIT) framework.
Density ratio modeling for covariate shift.
Renewable updating strategy using summary-level information.
Conformal prediction for uncertainty quantification.

Main Results:

ReFIT enhances predictive accuracy and uncertainty quantification compared to single-source models.
The framework is robust to model misspecification and source-target shift.
Conformal prediction intervals narrow with accumulating data, improving efficiency.
ReFIT improved breast cancer prediction for a Hispanic population using EHR data.

Conclusions:

ReFIT offers a scalable, privacy-preserving, and adaptive solution for distributed biomedical data.
The framework effectively integrates information from multiple, periodically updated sources.
ReFIT demonstrates significant improvements in prediction and uncertainty quantification, particularly for underrepresented groups.